Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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A Sharp Cramer-Rao type Lower-Bound for Median-Unbiased Estimators

  • So, Beong-Soo (Department of Statistics, Ewha Womens University, Seodaemun, Seoul 120-750)
  • Published : 1994.06.01
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Abstract

We derive a new Cramer-Rao type lower bound for the reciprocal of the density height of the median-unbiased estimators which improves most of the previous lower bounds and is attainable under much weaker conditions. We also identify useful necessary and sufficient condition for the attainability of the lower bound which is considerably weaker than those for the mean-unbiased estimators. It is shown that these lower bounds are attained not only for the family of continuous distributions with monotone likelihood ratio (MLR) property but also for the location and scale families with strong unimodal property.

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References

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